ES-100 Two-Dimensional Equilibrium
SFx = 0
SFy = 0
SM = 0
For an object to be in equilibrium in two-space three scalar equations of static equilibrium must be satisfied...

SFx or SFy = 0
SMA = 0
SMB = 0
Since any three independent equations of equilibrium may be used, an alternate would be the set of equations shown where A and B are two points on the body.

SMA = 0
SMB = 0
SMC = 0
Or alternately, three moment equations may be used.
Note: Any three non-redundant equations may be used.

Note: Sometimes one equation is trivially satisfied.
For example, if there are no forces in the x-direction that equation is automatically satisfied and only two equations are left to solve the problem.

A mass of 10kg is hung from two ropes, AB and BC. Find the tension in each rope. A statics problem is usually stated with a description, and, if necessary, a diagram.
Lets examine an example...

The associated space diagram is shown here.

The space diagram is converted to a free body diagram. For a free body diagram a point or body is isolated and all forces on it are indicated.

SFx = 0 = FBC cos( 45° ) - FAB cos( 30° ) ( 1 )
SFy = 0 = FBC sin( 45° ) + FAB sin( 30° ) - 98.1 ( 2 )
The force equilibrium equations in the x and y directions may then be written...

FBC = 1.2 FAB from (1)
FAB (.707) + FAB(.500) = 98 from (2)
FAB = 72.7 N
FBC = 87.2 N
Solving for FAB and FBC...

Note: In this case the sum of the moments equation is automatically satisfied since all forces pass through one point.

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